vertices(+ or - 7 ,o) , e = 4/3

Vertices of what? What does e represent?

I will assume you meant:

vertices are (7,0) and (-7,0) with e = 4/3

you must be talking about a horizontal hyperbola with an eccentricity of 4/3

for a hyperbola e > 1 and e = c/a
c/a = 4/3
so we could have c = 4, and a = 3
but since the vertex is (7,0) a must be 7 in our equation
so c/a = 4/3 = (28/3) / 7

c= 28/3 , a=7
in a hyperbola:
a^2 + b^2 = c^2
49 + b^2 = 784/9
b^ = 784/9 - 49
= 343/9

how about

x^2/49 - y^2/(343/9) = 1

To find the value of "o" in the equation "vertices(+ or - 7, o), e = 4/3," we need some additional information. The given equation has two variables, "o" and "e." However, there is no relationship or equation provided that can help us solve for "o" directly.

If you have any additional information or equations related to "o" or "e," please provide them so that we can proceed with finding the value of "o."